Answer: B. The minimum y-value of g(x) is -3.
Explanation:
Based on the given functions:
f(x) = 3 - 3
g(x) = 7x² - 3
The y-value of f(x) is constant at -3, regardless of the value of x. Therefore, f(x) does not have a minimum y-value, and option A is incorrect.
The y-value of g(x) is determined by the quadratic term 7x². Since the coefficient of x² is positive (7), the parabola opens upwards, indicating that g(x) has a minimum y-value. To find the minimum value of g(x), we can look at the vertex of the parabola, which occurs when x = -b/2a in the quadratic equation ax² + bx + c. In this case, a = 7 and b = 0, so the vertex is at x = -0/2(7) = 0. Substituting x = 0 into g(x), we find: g(0) = 7(0)² - 3 = -3 Therefore, the minimum y-value of g(x) is -3, and option B is correct.
Option C, stating that g(x) has the smallest possible y-value, is incorrect because the y-value of g(x) can be larger than -3 depending on the value of x.
Option D, stating that f(x) has the smallest possible y-value, is incorrect because f(x) does not have a minimum y-value as it is constant at -3.
Therefore, the correct answer is B. The minimum y-value of g(x) is -3.